Getting the passport number wrong is possible(as this thread demonstrates), but more difficult than a lot of folk would think.
Passports, like bank accounts numbers have a check digit which is meant to avoid such mistakes and the algorithm used is often tested on the entry field of booking systems.
I had to calculate a dummy one once for a genuine and innocuous reason and although the algorithm itself is fairly straight-forward, inventing a number that would be accepted by the system still took a few tries.